I am in a similar position to yourself, watched the NFL years ago on C4 but fell away from the sport. Back then I used to really like the Dolphins and through the years on occasion would look out for their results. I came to this forum not knowing what team to support as although I still saw the Dolphins as my most likely choice part of me wanting to pick a team that had never won the Super Bowl. In my thread I got a lot of good advice and I've managed to bring my choices down to three teams which is either the Bears, Dolphins or Giants.

Bears were suggested to me in my thread and appealed to me as there is connections to things I love like

-I'm a big Batman fan, I have thousands of comics and the Dark Knight trilogy used Chicago as Gotham
-I'm a Glasgow Rangers fan and their nickname is the Teddy bears which links to the Bears
-Rangers play in blue and used to have an orange strip which I loved and the Bears have those colours

As for the Giants I also follow Ice Hockey and the New York Rangers so to follow the New York Giants would make sense as if I ever go to America there is a good chance it'll be to New York to watch the NYR play which means I could take in a Giants game too. Like Glasgow Rangers and New York Rangers the Giants play in Blue White and Red. The one thing that puts me off the Giants is that they are a successful franchise whereas the Bears and Dolphins not so much. I wanted a team who I could say I followed through some of the bad times and into the good and not be a gloryhunter.

Try thinking of things that connect you to teams, logos you like, colours you like, players you like and narrow it down. The way I started was to eliminate teams I knew I wouldn't follow for one reasons or another like too successful or teams who have changed name and been relocated like Patriots, Cowboys, Steelers, Raiders, Chargers and Rams.